Complete reducibility

Jean-Pierre Serre

Séminaire Bourbaki (2003-2004)

  • Volume: 46, page 195-218
  • ISSN: 0303-1179


The notion of complete reducibility of a linear representation Γ 𝐆𝐋 n can be defined in terms of the action of Γ on the Tits building of 𝐆𝐋 n . An analogous definition can be given for any reductive group. We shall see how this translates in topological terms, and what applications can be obtained.

How to cite


Serre, Jean-Pierre. "Complète réductibilité." Séminaire Bourbaki 46 (2003-2004): 195-218. <>.

abstract = {La notion de complète réductibilité d’une représentation linéaire $\Gamma \rightarrow \mathbf \{GL\}_n$ peut se définir en termes de l’action de $\Gamma $ sur l’immeuble de Tits de $\mathbf \{GL\}_n$. Cela suggère une notion analogue pour tous les immeubles sphériques, et donc aussi pour tous les groupes réductifs. On verra comment cette notion se traduit en termes topologiques et quelles applications on peut en tirer.},
author = {Serre, Jean-Pierre},
journal = {Séminaire Bourbaki},
keywords = {reductive groups; spherical buildings; complete reducibility},
language = {fre},
pages = {195-218},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {Complète réductibilité},
url = {},
volume = {46},
year = {2003-2004},

AU - Serre, Jean-Pierre
TI - Complète réductibilité
JO - Séminaire Bourbaki
PY - 2003-2004
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 46
SP - 195
EP - 218
AB - La notion de complète réductibilité d’une représentation linéaire $\Gamma \rightarrow \mathbf {GL}_n$ peut se définir en termes de l’action de $\Gamma $ sur l’immeuble de Tits de $\mathbf {GL}_n$. Cela suggère une notion analogue pour tous les immeubles sphériques, et donc aussi pour tous les groupes réductifs. On verra comment cette notion se traduit en termes topologiques et quelles applications on peut en tirer.
LA - fre
KW - reductive groups; spherical buildings; complete reducibility
UR -
ER -


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